A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of:

Question

A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of: (A) 125 m/s (B) 250 m/s (C) 500 m/s (D) 1000 m/s

Tardigrade Admin · Accepted Answer

A normal mode of an oscillating system is a motion in which all particles of the system move sinusoidally with the same frequency. In general,

pt h

mode of a string fixed at ends has frequency.

n = \frac{p v}{2 l}

p = 1, 2, 3..

where

v

is velocity of wave and I is length of string. In fourth normal mode,

p = 4

∴

n = \frac{4 v}{2 l}

Given,

n = 500 Hz, l = 2 m

Hence,

500 = \frac{4 v}{2 \times 2}

or

v = \frac{500 \times 4}{4} = 500 m / s

Q. A string of length 2m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500Hz, then the waves would travel on it with a velocity of:

125 m/s

250 m/s

500 m/s

1000 m/s

Q. A string of length $2 m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 Hz$ , then the waves would travel on it with a velocity of: