A 4.00-m long string,clamped at both ends,vibrates at 2.00 × 10² Hz.If the string resonates in six segments,what is the speed of transverse waves on the string?
A)100 m/s
B)133 m/s
C)267 m/s
D)328 m/s
E)400 m/s

Question

Quizplus · Accepted Answer

First, we need to find the wavelength of the wave on the string using the given information that the string resonates in six segments.

A string can vibrate in different modes or segments, and the wavelength in each mode is determined by the length of the string and the number of segments. In this case, we have six segments, which means the wavelength is four times the length of the string divided by six:

λ = (4/6)L = (2/3)L

Next, we can use the formula for the speed of a wave on a string:

v = fλ

where v is the speed of the wave, f is the frequency (given as 2.00 × 10² Hz), and λ is the wavelength we just calculated.

Plugging in the numbers gives:

v = (2.00 × 10² Hz)(2/3)(4.00 m) 
v = 267 m/s

Therefore, the best choice is C) 267 m/s.

A 400-M Long String,clamped at Both Ends,vibrates at 2