Use the following passage for the next three (3) questions. A student attaches a

Question

Use the following passage for the next three (3) questions. A student attaches a string to a vibrator at one end and a mass M at the other. He clamps the vibrator firmly on the lab table and hangs the mass over a frictionless pulley as shown in Figure 3 below. The distance from the pulley to the vibrator is 1.0 m. The speed of a wave on the string is determined by the following equation: v = Squareroot F_T/mu Where F_T is the tension force on the string and mu is the linear density of the string. The student is using the same string in all his experiments. The string used has a linear density of 2.5 times 10^-4 kg/m. When the student slowly increases the frequency, he observes the first standing wave (shown in figure 4 below) at a certain frequency, f_o. What is the wavelength for the standing wave with frequency f_o? a. 1.0 m b. 2.0 m c. 0.5 m d. 4.0 m e. 0.25 m In one experiment the student hangs a mass M of 2.5 kg at the end of the string. Determine the frequency f_o for the first standing wave. a. 100 Hz b. 626 Hz c. 313 Hz d. 157 Hz If the student measures the frequency of the first standing wave (f_o) to be 165 Hz, what is the frequency of second possible standing wave? a. 330 Hz b. 495 Hz c. 660 Hz d. 825Hz e. 83 Hz

Explanation / Answer

(1) ans

Given that

length L=1 m

basing on the concept of the speed of the transverse wave

now we find the wavelength

wavelength =2L=2*1=2m

the correct option is b

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Given that

mass m=2.5 kg

tension T=mg=2.5*9.8=24.5 N

now we find the speed of the transverse wave

speed V=[24.5/2.5*10^-4]^1/2=3.13*10^2 m/s

now we find the frequency

frequency f=3.13*10^2/2=156.5 Hz=157 Hz

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Given that

frequency of first standing wave f1=165 Hz

now we find the frequency of second standing wave

frequency f2=2f1=2*165=330 Hz

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