First slide

Superposition of waves

Question

Vibrating tuning fork of frequency n is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through 8.75 cm, the intensity of sound changes from a maximum to minimum. If the speed of sound is 350 m/s. Then n is

Moderate

A

500 Hz
B

1000 Hz
C

2000 Hz
D

4000 Hz

Solution

When the piston is moved through a distance of 8.75cm, the path difference produced is $2 \times 8 .75 cm = 17 .5 cm$ . This must be equal to $\frac{λ}{2}$ for maximum to change to minimum. $∴ \frac{λ}{2} = 17 .5 cm \Rightarrow λ = 35 cm = 0 .35 m$
So, $v = nλ \Rightarrow n = \frac{v}{λ} = \frac{350}{0 .35} = 1000 Hz$

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