SATHEE: Wave Motion 2 Question 2

Wave Motion 2 Question 2

2. A string $2.0 m$ long and fixed at its ends is driven by a $240 H z$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

(Main 2019, 9 April II)

(a) $180 m / s, 80 H z$

(b) $320 m / s, 80 H z$

(d) $180 m / s, 120 H z$

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Answer:

Correct Answer: 2. (b)

Solution:

Frequency of vibration of a string in $n$ th harmonic is given by

$f_{n} = n \cdot \frac{v}{2 l}$

where, $v =$ speed of sound and $l =$ length of string.

Here, $f_{3} = 240 H z, l = 2 m$ and $n = 3$

Substituting these values in Eq. (i), we get

$∴ 240 = 3 \times \frac{v}{2 \times 2} \Rightarrow v = \frac{4 \times 240}{3} = 320 m s^{- 1}$

Also, fundamental frequency is

$f = \frac{f_{n}}{n} = \frac{f_{3}}{3} = \frac{240}{3} = 80 H z$

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Wave Motion 2 Question 2

2. A string 2.0m long and fixed at its ends is driven by a 240Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

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2. A string $2.0 m$ long and fixed at its ends is driven by a $240 H z$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is