1. Using a 2 meter long slinky that is anchored on both ends, what is the frequency of the 2nd mode ofvibration, given a velocity of c = 500 m/sec.2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st modeof vibration, given a velocity of c = 500 m/sec.3. The vocal tract tube measures approximately 20 cm (0.2 meters) in length. What would be the 3rdmode of vibration during production of a vowel with an open mouth posture. Use formula for 1/4wave resonator and c=343 m/sec (velocity for sound transmission in air).4. You pick up an empty 16 oz. plastic coke bottle and blow a steady airstream over the top edge of thebottle's mouth to set the air in the bottle into resonance. What is the frequency of the 1" mode for thebottle? (Hint: you'll need a metric ruler for this question).5. The Empire State Building in NYC is approximately 440 meters in height. The superstructure of thebuilding is made of steel which means that energy will be transmitted through the buildings core at 1500m/sec. If the building is being blasted and buffeted by a strong wind storm, at what frequency will thebuilding sway in it's 1st mode of vibration. (Hint: think about what type of a resonator a building could be)

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Description: 1. Using a 2 meter long slinky that is anchored on both ends, what is the frequency of the 2nd mode ofvibration, given a velocity of c = 500 m/sec.2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st mod

We know that the relation between the frequency and wavelength and velocity is given as ' c = fλf=…

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2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st mode of vibration, given a velocity of c 500 m/sec.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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1. Using a 2 meter long slinky that is anchored on both ends, what is the frequency of the 2nd mode of
vibration, given a velocity of c = 500 m/sec.
2. Using a 1 meter long slinky that is anchored at only one end, what is the frequency for the 1st mode
of vibration, given a velocity of c = 500 m/sec.
3. The vocal tract tube measures approximately 20 cm (0.2 meters) in length. What would be the 3rd
mode of vibration during production of a vowel with an open mouth posture. Use formula for 1/4
wave resonator and c=343 m/sec (velocity for sound transmission in air).
4. You pick up an empty 16 oz. plastic coke bottle and blow a steady airstream over the top edge of the
bottle's mouth to set the air in the bottle into resonance. What is the frequency of the 1" mode for the
bottle? (Hint: you'll need a metric ruler for this question).
5. The Empire State Building in NYC is approximately 440 meters in height. The superstructure of the
building is made of steel which means that energy will be transmitted through the buildings core at 1500
m/sec. If the building is being blasted and buffeted by a strong wind storm, at what frequency will the
building sway in it's 1st mode of vibration. (Hint: think about what type of a resonator a building could be)

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