When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones.Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones元P, =A, sin (2uft + 1) and P, = A2 sin (2nft + dp2) , where - s41,.427, then the resulting tone heard by a listener can be written as P = A sin (2nft + 4), whereA, sin 4, + A, sin p24 = arctan(A, cos 4, + A, cos42)² + (A, sin d, + A2 sin 2) 2 . Complete parts a and b.and A =1A, cos , + A2 cos 42(a) Calculate A and p if A, = 0.0009, , =0.057, A2=0.004, and p2 = 0.68. Also find an expression for P = A sin (2xft + 4p) if f= 220.A =(Do not round until the final answer. Then round to five decimal places as needed.)(Do not round until the final answer. Then round to five decimal places as needed.)Find an expression for P = A sin (2xft + 4) if f= 220.P=(Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.)(b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?Choose the correct graph below. All graphs are [0,.01] by [-.01,.01].O A.OB.OC.OD.QQ

Answered: Image /qna-images/answer/de490276-ebb8-4e3e-a240-0229c392f4d2.jpg

When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones. Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones P, = A, sin (2xft + b1 ) and P, = A2 sin (2xft + 2), where -s.2 s, then the resulting tone heard by a listener can be written as P = A sin (2xft + 4»), where A, sin p, + Az sin z = arctan A, cos 4, + Az cos Þ2 and A = (A, cos 41 + Az cos 2) ² + (A, sin 4, + A2 sin 2) ² . Complete parts a and b. a) Calculate A and if A, = 0.0009, Þ1 = 0.057, A2=0.004, and Þ2 = 0.68. Also find an expression for P = A sin (2xft + 4) if f = 220. Do not round until the final answer. Then round to five decimal places as needed.) (Do not round until the final answer. Then round to five decimal places as needed.) Find an expression for P = A sin (2xft + 4p) if f= 220. (Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.) (b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?

When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones. Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones P, = A, sin (2xft + b1 ) and P, = A2 sin (2xft + 2), where -s.2 s, then the resulting tone heard by a listener can be written as P = A sin (2xft + 4»), where A, sin p, + Az sin z = arctan A, cos 4, + Az cos Þ2 and A = (A, cos 41 + Az cos 2) ² + (A, sin 4, + A2 sin 2) ² . Complete parts a and b. a) Calculate A and if A, = 0.0009, Þ1 = 0.057, A2=0.004, and Þ2 = 0.68. Also find an expression for P = A sin (2xft + 4) if f = 220. Do not round until the final answer. Then round to five decimal places as needed.) (Do not round until the final answer. Then round to five decimal places as needed.) Find an expression for P = A sin (2xft + 4p) if f= 220. (Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.) (b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Two speakers (A and B) lie on the y-axis, 4.0m apart. They emit exactly the same 280 Hz tone in…

A: speed of the sound v = 340 m/s Ferquncy (f) = 280 Hz

Q: There are 4 identical dogs barking with identical sound intensity levels of 92 dB as measured by a…

Q: The speed of sound in room temperature (20°C) air is 343 m/s; in room temperature helium, it is 1010…

Q: The longitudinal displacement of a mass element in a medium as a sound wave passes through it is…

Q: A trumpet creates a sound intensity level of 9.80 x 10* dB at a distance of 1.10 m. (a) What the…

A: Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Q: The African cicada is the world’s loudest insect, producing a sound intensity level of 107 dB at a…

Q: Suppose a sound has intensity I that is 100,000 times greater than the intensity of the quietest…

Q: Speakers A and B are vibrating in phase. They are directly facing each other, are 1.33 m apart, and…

A: distance between the two speakers = 1.33 m frequency = 715 Hz speed of sound = 345 ms

Q: What is the decibel level of a sound that has an intensity of 57.5 x 10-5 W/m2? Assume the…

A: The sound intensity is The reference intensity is Find:Sound level for given sound intensity.

Q: A sound with a frequency of 3258Hz is perceived to be as -8.2dB. What is the intensity of the sound…

Q: You work at a building site and the noise level has been measured at 95 dB. You need to wear…

Q: A 3.00 m long air column is open at both ends. The frequency of a certain harmonic is 410 Hz, and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the decibel level of a sound that has an intensity of 87 x 10-5 W/m?? Assume the standard dB…

Q: The sound intensity at a certain location is 4.0×10-6 W/m2. What is the sound intensity level at…

A: Given : Intensity at certain level (I) = 4.0×10-6 W/m2. threshold intensity (I0) = 1 x 10-12…

Q: Problem 1: An audio engineer takes decibel readings at distances of r = 14 m and r, = 22 m from a…

Q: An audio engineer takes decibel readings at distances of r1=11m and r2=23m from a concert stage…

A: Part (a) Sound level is given by: β= 10*log (I1/I0) β = Sound level of at r1 distance from speaker =…

Q: Speakers A and B are vibrating in phase. They are directly facing each other, are 6.07 m apart, and…

Q: A single sound source, measured at a particular point, produces a sound pressure level of 40.1…

Q: Two students hear the same sound and their eardrums receive the same power from the sound wave. The…

A: Given; Let there be two students A and B. Both receives the same power from sound wave i.e. PA =…

Q: Two students hear the same sound and their eardrums receive the same power from the sound wave. The…

A: Given that First Intensity I1 = 0.79 W/m2 Second intensity I2 = (1.18)(0.79) W/m2 = 1.18I1 Diameter…

Q: For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has…

Q: A open end tube will set up a standing sound wave when there is an antinode at both ends of the…

Q: Two sound waves have intensities I₁ and I2. What is difference of the sound levels in dB? I₁ =…

Q: mplified through a sound system the amplified sound has a sound intensity level that is 12.2 dB…

A: We have givenA sound system the amplified sound has a sound intensity level that is 12.2 dB greater…

Q: Two students are standing the same distance from a source of sound. The first student receives a…

Q: If a person speaks with an intensity of 0.701 μ W/m2, what is the sound intensity level in…

Q: single dog barks at a sound intensity level of β = 95 dB. A) Another dog runs up beside the first…

Q: a noise level meter reads the sound level in a room to be 85 dB. What is the intensity of sound in…

A: Given sound level 85dB We know sound level in dB is dB=10log( I/I0) where l is intensity of sound…

Q: A sound wave having a frequency of 345 Hz travels through air at 20 °C. The decibel level at a…

A: Given: Frequency of sound waves = 345 Hz Decibel level at distance 16.3 m = 86.5 dB Density of air =…

Q: An audio engineer takes decibel readings at distances of r1 = 13 m and r2 = 21 m from a concert…

Q: A speaker puts out a constant sound with a power of P = 15 milliwatts and frequency fs = 256 Hz.…

A: Power (P) = 0.015 W fs = 256 Hz

Q: A sound wave has frequency f and velocity VM in a particular solid medium. What is its wavelength in…

A: Given: The frequency of the wave is 400 Hz. The speed of the wave is 3720 m/s.

Q: The sound intensity level 3.6-m from a power saw is 101 dB. At what distance will the sound be a…

Q: Problem 21: A single dog barks at a sound intensity level of ß= 84 dB. andomized Variables = 84 dB…

Q: Problem 4. A point source emits sound waves uniformly in all directions. At distance 90.0 m from the…

Q: What is the decibel level of a sound that has an intensity of 10.4 x 10-5 W/m2? Assume the…

A: The sound intensity is The reference sound intensity is Find:Sound level for given sound intensity.

Q: a) The sound level of a jet at take off is 140 dB, while the level of a normal conversation is 50…

A: Given: Reference Intensity,I0=10-12W/m2Sound Intensity Level,β1=140dBSound Intensitty Level,β2=50dB…

Q: Suppose that a public address system emits sound uniformly in all directions and that there are no…

A: The formula for the intensity in terms of power and surface area is:

Q: The intensity level in decibels is defined as 10 log10(I/I0), where I0 is a reference intensity…

A: Given data: Intensity level in decibels dB = 10 log10(I/I0) Here I0 = 10-12 W/m2 The intensity of…

Q: A.) Find the loudness L, in decibles (dB), of a trombone given the intensity is 1010I0 B.) Find the…

A: A) The trombone’s loudness in decibel can be determined as, Here, I and I0 represent sound’s…

Concept explainers

Properties of sound

A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).

Quality Of Sound

A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.

Categories of Sound Wave

People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.

Question

100%

When two sources located at different positions produce the same pure tone, the human ear will often hear one sound that is equal to the sum of the individual tones.
Since the sources are at different locations, they will have different phase angles p. If two speakers located at different positions produce pure tones
元
P, =A, sin (2uft + 1) and P, = A2 sin (2nft + dp2) , where - s41,.427, then the resulting tone heard by a listener can be written as P = A sin (2nft + 4), where
A, sin 4, + A, sin p2
4 = arctan
(A, cos 4, + A, cos
42)² + (A, sin d, + A2 sin 2) 2 . Complete parts a and b.
and A =
1
A, cos , + A2 cos 42
(a) Calculate A and p if A, = 0.0009, , =0.057, A2=0.004, and p2 = 0.68. Also find an expression for P = A sin (2xft + 4p) if f= 220.
A =
(Do not round until the final answer. Then round to five decimal places as needed.)
(Do not round until the final answer. Then round to five decimal places as needed.)
Find an expression for P = A sin (2xft + 4) if f= 220.
P=
(Use integers or decimals for any numbers in the expression. Round to five decimal places as needed.)
(b) Graph Y, = P and Y2 = P, +P2 on the same coordinate axes over the interval [0,.01]. Are the two graphs the same?
Choose the correct graph below. All graphs are [0,.01] by [-.01,.01].
O A.
OB.
OC.
OD.
Q
Q

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

The loudness of sound can be measured on a decibel scale. The sound level L (in decibels) of a sound is given by 0-12 W/m². The L=10 log where I is the intensity of the sound (in watts per square meter, W/m²) and I = 10 1 intensity, I, of a whisper is 10-10 W/m². Find the decibel value of this sound. The decibel value of this sound is. (Simplify your answer. Type an integer or a fraction.) GEREID
A safety technician measures the sound volume level inside the office of the engineer supervising the and calculates L1=72 dB. As an excavator is working outside the office, he again measures the volume level and finds L2=86 dB. What is the sound volume level of the excavator alone within the office space?
The speed of sound in room temperature (20°C) air is 343 m/s; in room temperature helium, it is 1010 m/s. The fundamental frequency of an open-closed tube is 315 Hz when the tube is filled with air. What is the fundamental frequency if the air is replaced with helium?
Problem #4: What sound intensity level in dB is produced by earphones that create an intensity of 4.00 x 10-2 W/m2? Problem #5: What is the intensity of a sound that has a level 7.00 dB lower than a 4.00 × 10–9 W/m2 sound? Problem #6: What is the intensity of a sound that is 3.00 dB higher than a 4.00 × 10–9 W/m2 sound? Problem #7: If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
With a sound level meter, you measure the sound pressure level to 95 dB. A sound source is a work machine that is on a hard surface, i.e. it can be thought of as sending sound to the surface of a hemisphere. The device is 20 m away from you. Calculate the power of the sound produced by the device in watts to one decimal place. Also Calculate the sound pressure level to the nearest decibel if your distance from the device doubles.
A concert loudspeaker suspended high off the ground emits 45 W of sound power. What is the sound intensity that reaches the an audience member 80 m away from the speaker? units: How many decibels does the audience member hear? units:
A sound wave having a frequency of 266 Hz travels through air at 20 °C. The decibel level at a distance of 21.3 m from the source is measured to be 77.4 dB. What is the maximum displacement of air molecules at that location? Assume the density of air is 1.20 kg/m³ and that the source produces spherical wave fronts. Express the displacement as a number having the units of mirco meters. 1 micro meter = 1 x 10-6 m. For example, If your calculated answer were 1.873 x 10-7 m, your entry would be the number 0.187 7.13
A sound has an of intensity 2.0*10-4 W/m2 and has a sound level of 83.0 dB. If you double the intenisty how much does the sound level go up? 0.5 dB 1.0 dB 1.5 dB 2.0 dB 2.5 dB 3.0 dB 3.5 dB
You are at BNA (Nashville Airport) watching commercial airliners take off. At a distance of 1,020.6 away from the plane, you record a sound intensity level of 73.4 decibels. If you move such that the new sound intensity level is 88.07 decibels, how far are you away from the plane (in meters)?
You are at BNA (Nashville Airport) watching commercial airliners take off. At a distance of 1,364.2 away from the plane, you record a sound intensity level of 69.31 decibels. If you move such that the new sound intensity level is 91.34 decibels, how far are you away from the plane (in meters)?
Suppose that sound is emitted uniformly in all directions by a public address system. The intensity at a location 28.0 m away from the sound source is 2.80 x 10-4 W/mz. What is the intensity at a spot that is 84.0 m away?
Problem #3: What intensity level dB in does a sound of 3. 04 × 10–4 W/m2 correspond to?