A wave on a string has a wavelength of 0.90 m at a frequency of 600 Hz.If a new wave at a frequency of 300 Hz is established in this same string under the same tension,what is the new wavelength?
A)2.7 m
B)1.8 m
C)0.45 m
D)0.30 m

Question

Quizplus · Accepted Answer

The formula for the wavelength of a wave on a string is:
wavelength = (tension/linear density) x (1/frequency)^0.5
Since the tension and linear density of the string are the same for both waves, we can set the two wavelength equations equal to each other and solve for the new wavelength:
wavelength1 = wavelength2
(tension/linear density) x (1/frequency1)^0.5 = (tension/linear density) x (1/frequency2)^0.5
Simplifying and solving for wavelength2, we get:
wavelength2 = wavelength1 x (frequency1/frequency2)^0.5
Plugging in the values, we get:
wavelength2 = 0.90 m x (600 Hz/300 Hz)^0.5
wavelength2 = 0.90 m x 2^0.5
wavelength2 = 1.8 m
Therefore, the new wavelength is 1.8 m, which corresponds to choice B.

A Wave on a String Has a Wavelength of 0