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1.You have five tuning forks that oscillate at close but different frequencies. What are the
(a) Maximum and
(b) Minimum number of different beat frequencies you can produce by sounding the forks two at a time, depending on how the frequencies differ?
2. Two tuning forks have frequencies of 256 and 260 Hz. If the forks are vibrating at the same time, what is the beat frequency?
3.The assistant adjusts the tension in the same piano string, and a beat frequency of 2.00 Hz is heard when the note and the tuning fork are struck at the same time.
(a) Find the two possible frequencies of the string.
(b) Assume the actual string frequency is the higher frequency. If the piano tuner runs away from the piano at 4.00 m/s while holding the vibrating tuning fork, what beat frequency does he hear?
(c) What beat frequency does the assistant on the bench hear? Use 343 m/s for the speed of sound.
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4.A tuning fork attached to a stretched wire generates transverse waves. The vibration of the fork is perpendicular to the wire. Its frequency is 400 Hz, and the amplitude of its oscillation is 0.50 mm. The wire has linear mass density of 0.01 kg/m and is under a tension of 1kN. Assume that there are no reflected waves.
(a) Find the period and frequency of waves on the wire.
(b) What is the speed of the waves?
(c) What are the wavelength and wave number?
(d) Write a suitable wave function for the waves on the wire.
(e) Calculate the maximum speed and acceleration of a point on the wire.
(f) At what average rate must energy be supplied to the fork to keep it oscillating at a steady amplitude?
5.A tuning fork of frequency 440 Hz is attached to a long string of linear mass density 0.01 kg m-1 kept under a tension of 49 N. The fork produces transverse waves of amplitude 0.50 mm on the string.
(a) Find the wave speed and the wavelength of the waves.
(b) Find the maximum speed and acceleration of a particle of the string.
(c) At what average rate is the tuning fork transmitting energy to the string?
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