When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm.When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:
A)200 Hz and 20 cm
B)141 Hz and 10 cm
C)100 Hz and 20 cm
D)100 Hz and 14 cm
E)50 Hz and 14 cm

Question

Quizplus · Accepted Answer

The speed of the wave on the string is given by the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. Since the frequency is constant at 100 Hz, and the wavelength is initially 10 cm, we can solve for the speed: 
v = fλ = (100 Hz)(10 cm) = 1000 cm/s

When the tension in the string is doubled, the speed of the wave will also double (assuming the mass per unit length remains the same). So the speed of the wave is now: 
v' = 2v = 2000 cm/s

To find the new wavelength, we can use the equation v' = f'λ', where f' is the new frequency: 
2000 cm/s = f'(λ')

We know that the new frequency f' is greater than 100 Hz, since the speed has increased. We can try the answer choices:

A) 200 Hz and 20 cm 
Using f' = 200 Hz, we get λ' = v'/f' = 2000/200 = 10 cm 
This matches the initial wavelength, so this is not the correct answer.

B) 141 Hz and 10 cm 
Using f' = 141 Hz, we get λ' = v'/f' = 2000/141 = 14.2 cm 
This is close to the initial wavelength, but not quite there.

C) 100 Hz and 20 cm 
Using f' = 100 Hz, we get λ' = v'/f' = 2000/100 = 20 cm 
This does not match the initial wavelength, so this is not the correct answer.

D) 100 Hz and 14 cm 
Using f' = 100 Hz, we get λ' = v'/f' = 2000/100 = 20 cm 
This is the same as the initial wavelength, which means it must be the answer.

E) 50 Hz and 14 cm 
Using f' = 50 Hz, we get λ' = v'/f' = 2000/50 = 40 cm 
This does not match the initial wavelength, so this is not the correct answer.

Therefore, the answer is D: 100 Hz and 14 cm.

When a 100-Hz Oscillator Is Used to Generate a Sinusoidal