1) Suppose we have an air column 80cm long with one open end and one closed end. (a) Find (i.e. derive) an expression for the resonant frequencies of the air column in terms of the length L of the air column, the speed of sound v, and the harmonic number n. Don't simply write the equation – show me how you obtain it by sketching several resonant standing waves.
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- A string of mass 0.50 kg and a length 3.0 meters is clamped on both ends. If the tension in the string is 25 newtons, what are the lowest 3 natural frequencies of oscillation of the string? For each case, include a sketch of the standing wave pattern.An 80.00 cm guitar string has a mass of 3.25g. It has been tuned so that its fundamental mode of oscillation has a frequency of 256 Hz. A) What wave speed is required on the string? B) What string tension is required? C) What is the wavelength of the sound waves produced in the surrounding air at 20 degrees Celcius? D) Assume the string is isotropically emitting a total acoustic power of 8.5 mW, determine the sound level 22m away? (assume a point source)A tunnel under a river is 1.80 km long. (a) At what frequencies can the air in the tunnel resonate? (Use n to represent the harmonics where n = 1, 2, 3, . Frequencies are in Hz. Do not include units in your answer. Take the speed of sound in air to be 343 m/s.) fn = ? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.
- 4) You have a pipe that is closed at one end. In a 22.0 °C room, you find that two of the harmonics occur at 294 Hz and 490 Hz. a) What is the shortest possible length of this pipe? b) What would the fundamental frequency be if you opened the other end of the pipe?2. A very narrow slit of width a = 2.50µm is illuminated with light of wavelength 1 = 540.0 nm and a diffraction pattern is observed on a screen D=1.25 m from the slit. At the screen, how far from the optical axis, y2 , is the second minimum that appears on а. either side of the central maximum? b. At the screen, how far from the optical axis, ymax is the furthest minimum that appears on either side of the central maximum?A transverse wave in a string has the form y= 6.3 cos pi (0.09 x +2t), where x is in centimeters and t is in seconds. A) Find: The maximum amplitude in centimeters ( with one decimal place)
- A taut string has a length of 2.60 m and is fixed at both ends. (a) Find the wavelength of the fundamental mode of vibration of the string. (b) Can you find the frequency of this mode? Explain why or why not.The equation for the displacement of a stationary wave on a string is given by y = 2 (sin 5πt)(cos 6πx), where x and y are in meters, and t is in seconds. Determine: b. the amplitude of the point P which lies at a distance of 75 cm from the end of the reflection!The trunk of a elephant may extend up to 2.3 m. It acts much like an organ pipe only open at one end when the elephant blows air through it. 1)Calculate the fundamental frequency of the sound the elephant can create with its trunk. (Express your answer to two significant figures.) 2)If the elephant blows even harder, the next harmonic may be sounded. What is the frequency of the first overtone? (Express your answer to two significant figures.)
- A 1m long string is pinned at both ends. The string is plucked, and a standing wave is created. The wave number is ? = 4? rad/m.a) Calculate the wavelength of the wave.b) If there are 5 nodes in the string, find their positions.Answers: • 0.5 m• Xn = {0, 0.25, 0.5, 0.75, 1}Consider standing waves in a pipe of length L = 3.5 m containing a column of air. The speed of sound in the columns is v. = 334 m/s. Each of the standing wave images provided may represent a case for which one or both ends are open. ▷ A 20% Part (a) Select the image from the options provided showing the gas pressure for the third harmonic of a pipe with two open ends. Grade Summary Deductions Potential 0% 100% Submissions о Attempts remaining: 100 (0% per attempt) detailed view O O Submit Hint Feedback I give up! Hints: 0 for a 0% deduction. Hints remaining: 0 Feedback: A 20% Part (b) Calculate the wavelength 3 in m for the third harmonic in the pipe with two open ends. ӨThe 2nd harmonic of a string of length 40cm and linear mass density 2.7g/m has the same frequency as the 5tn possible harmonic of a closed pipe of length 0.9m. Find the tension in the string. N **Use 340 m/s for the speed of sound in air.