Question

The mass of a string is 5.5 × 10-3 kg, and it is stretched so that the tension in it is 230 N. A transverse wave traveling on this string has a frequency of 160 Hz and a wavelength of 0.66 m. What is the length of the string?

Answer 1

Answer:

The length of the string is 0.266 meters.

Explanation:

It is given that,

Mass of the string, $m=5.5\times 10^{-3}\ kg$

Tension in the string, T = 230 N

Frequency of wave, f = 160 Hz

Wavelength of the wave, $\lambda=0.66\ m$

We need to find the length of the string. Let l is the length of the string. The speed of a transverse wave is given by :

$v=\sqrt{\dfrac{T}{M}}$

M is the mass per unit length, M = m/l

$v=\sqrt{\dfrac{lT}{m}}$

$l=\dfrac{v^2m}{T}$

The velocity of a wave is, $v=\nu\times \lambda$

$l=\dfrac{(\nu\times \lambda)^2m}{T}$

$l=\dfrac{(160\ Hz\times 0.66\ m)^2\times 5.5\times 10^{-3}\ kg}{230\ N}$

l = 0.266 meters

So, the length of the string is 0.266 meters. Hence, this is the required solution.                  

Answer 2

Answer:

L = 0.275 m

Explanation:

velocity of transverse wave in a stretched string is  given as

$v =\sqrt \frac{T}{\mu}$

where T = tension = 230N

μ = linear density

$μ = \frac[m}{L}$

where length L is in meters

Velocity = $n\lambda$

so we have after equating both value of velocity

$\sqrt \frac{T}{\mu} = n\lambda$

$\frac{T}{\mu} =(n\lambda)^{2}$

μ  = $\frac{T}{(n\lambda)^{2}}$

μ = $\frac{230}{(160*0.66)^{2}}$

μ = 0.020 kg/m

but μ = $\frac[m}{L}$

so length of string is

L = $\frac{5.5*10^{-3}}{0.020}$

L = 0.275 m