A vibrating string of certain length under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. [2008]

Question

A vibrating string of certain length $l$ under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is [2008]

Smart Achievers · Accepted Answer

(1)

With increase in tension, the frequency produced by string increases. As the beats/sec decreases therefore frequency of tuning fork

$f = 3 (\frac{v}{4 l}) + 4 = 3 (\frac{340}{4 \times 0.75}) + 4 = 344 Hz$

Solution

1 344

2 336

3 117.3

4 109.3

Ans.
(1)

With increase in tension, the frequency produced by string increases. As the beats/sec decreases therefore frequency of tuning fork

$f = 3 (\frac{v}{4 l}) + 4 = 3 (\frac{340}{4 \times 0.75}) + 4 = 344 Hz$

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