112. A string, fixed on both ends, is 5.00 m long and has a mass of 0.15 kg. The tension if the string is 90 N. The string is vibrating to produce a standing wave at the fundamental frequency of the string. (a) What is the speed of the waves on the string? (b) What is the wavelength of the standing wave produced? (c) What is the period of the standing wave?

a) 55m/s

b)10m

c) 0.18 sec

Explanation:

a) In order to find the speed of the waves on the string can, we use the formula, i.e

v = sqrt (T/ μ)

where,

T = tension in the string

μ = linear density

μ linear density can be calculated by:

μ= m/L => 0.15/ 5 => 0.03 kg/m

v = sqrt (T/ μ)

v = sqrt ((90 / 0.03)    

v=  55 m/s

therefore,  the speed of the waves on the string is 55m/s

b)   the wavelength of the standing wave produced can be determined by

λ = 2L /n >( n=1 because the string is vibrating to produce a standing wave at the fundamental frequency)

λ = 2 x 5 /1

λ = 10m

therefore,  the wavelength of the standing wave produced is 10m

c) in order to find the period, lets first determine the frequency of standing waves.

f= v/ λ

f= 55 / 10

f= 5.5 Hz

next is to take the inverse of frequency as you know it is inversely proportional to period T

T= 1/f

T= 1/5.5

T= 0.18 s

thus, the period of the standing wave is 0.18 sec

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