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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?

2 Answers

1 vote

Answer:

L = 0.275 m

Step-by-step explanation:

velocity of transverse wave in a stretched string is given as


v =\sqrt (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 (T)/(\mu) = n\lambda


(T)/(\mu) =(n\lambda)^(2)

μ =
(T)/((n\lambda)^(2))

μ =
(230)/((160*0.66)^(2))

μ = 0.020 kg/m

but μ =
\frac[m}{L}

so length of string is

L =
(5.5*10^(-3))/(0.020)

L = 0.275 m

User Peter Macej
by
6.2k points
1 vote

Answer:

The length of the string is 0.266 meters.

Step-by-step explanation:

It is given that,

Mass of the string,
m=5.5* 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{(T)/(M)}

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


v=\sqrt{(lT)/(m)}


l=(v^2m)/(T)

The velocity of a wave is,
v=\\u* \lambda


l=((\\u* \lambda)^2m)/(T)


l=((160\ Hz* 0.66\ m)^2* 5.5* 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.

User Bondan Herumurti
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7.1k points