For the standing waves on the strings, we generate a standing wave on mode #5. T

Question

For the standing waves on the strings, we generate a standing wave on mode #5. The distance between the two end of string is 0.8 m. The distance between nodes is 0.16 m. What is the wave length of the wave on strings in meter.

In the standing wave experiment, we plan to measure the speed of the mechanical wave on the string. So we measure the frequency for each mode f , and the wave length of each mode l. The equation is f=v/l. To got speed v. we use linear fitting on the graph. The value on y axis is f. What is the value on x axis?

For the standing wave on mode #4, how many anti-nodes does it have?

For a wave on string, the distance of two end of the string is fixed. At the node #2, we know that distance of two nodes is 0.45 m and the frequency is 60 Hz. What frequency on Hz should you set to make the standing wave on mode #3.

Explanation / Answer

(1) dsitance between nodes= 0.16

wavelength= 2 (0.16) = 0.32 m

(b) value along x axis will be 1/wavelength

V= f/(1/wavelength) = f * wavelength

(c)for mode #4, there are 4 anti nodes

(d) for node #2 , distance between nodes=0.45m

so wavelength= 2(0.45)= 0.9m

frequency= 60Hz

wavel velocity= f *wavelength = 0.9* 60 = 54 m/s

also wavelength = 2l/n where n is the number of mode

0.9= 2l/2 => l=0.9 m

so waveength for third mode= 2l/3 = 2(0.9)/3 =0.6m

now v= f * wavelength

f= v/wavelength =54/0.6

f=90Hz

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