Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 103 kg/m and a tension of 80 N when both ends are fixed in place.
[Ques. 2] A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?
[Ques. 3] Superposition of waves can occur
a. in transverse waves.
b. in longitudinal waves.
c. in sinusoidal waves.
d. in all of the above.
e. only in (a) and (c) above.
[Ques. 4] Tuning forks 1, 2, and 3 each have slightly different frequencies.When 1 and 2 are sounded together, a beat frequency of 3 Hz results. When 2 and 3 are sounded together, a beat frequency of 5 Hz results. If the frequency of 1 is 100 Hz, which of the following cannot be the frequency of 3?
a. 92 Hz
b. 95 Hz
c. 98 Hz
d. 102 Hz
e. 108 Hz
[Ques. 5] A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?
a. 30 N
b. 45 N
c. 80 N
d. 8.9 N
e. 13 N
[Ques. 6] A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1 . When the tension is slowly increased the resonance condition disappears until tension T2 is reached, there being no resonances occurring between these two tensions. How many antinodes are there in this new resonance?
a. 3
b. 4, since all resonances in this situation have the same number of nodes
c. 5
d. 2, since resonances only involve whole wavelengths
e. 6, since resonances only involve whole wavelength
[Ques. 7] A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500-Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?
a. 0
b. 15
c. 29
d. 63
e. 250
[Ques. 8] Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material
a. with a low Young's modulus and a low density.
b. with a low Young's modulus and a high density.
c. with a high Young's modulus and a low density.
d. with a high Young's modulus and a high density.
e. composed of a metal-plastic laminate.
[Ques. 9] A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = smcos(kx t). Its velocity can be obtained from
a. /k
b. k/
c. k
d.
e. k
[Ques. 10] A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?
a. The speed of the waves traveling along the string.
b. The tension in the string.
c. The wavelength of the waves on the string.
d. All of the above.
e. None of the above.
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