Change in wavelength

[Primarygun]

If a wave with wavelength 1.5 cm and frequency 8Hz, is viewed through a stroboscope with 6Hz, what's the change of its wavelength?

My answer is not identical to what in my text book.

My thought is :there is no change of the wavelength, as the time given is enough for the wave to move over one wavelength.

[ed84c]

Ok

 

well. Its speed is f * lambada

so f lambada is 8*1.5= 12 m/s

 

The speed is constant.

 

so 12/6= 2cm.

 

Well thats my thinking anyway :-D

[DQW]

If a wave with wavelength 1.5 cm and frequency 8Hz' date=' is viewed through a stroboscope with 6Hz, what's the change of its wavelength?

My answer is not identical to what in my text book.

My thought is :there is no change of the wavelength, as the time given is enough for the wave to move over one wavelength.[/quote']I'm not terribly familiar with the working of stroboscopes, but I'm pretty sure that you do not have enough information ot say that there is sufficient time to view an entire wavelength. The question says that the strobe frequency is 6 Hz. This means that there are 6 viewign windows each second. The length of each viewing window could be any number from say, a nanosecond to just under one-sixth of a second. My guess is that you must assume the viewing windows to be infinitesimally small.

 

PS : What is the answer by the textbook ?

 

Edit : Do not answer that yet...let me make a suggestion first.

[Primarygun]

A hand stroboscope. It keeps moving with 6 Hz, but the wave moves with 8Hz.

A point I am absolutely certain about is : the wave viewed through the strob. is moving a bit forward slowly.

[DQW]

I get an answer of 6 cm but I'm not certain about it yet. What is the answer in the book?

[Primarygun]

0.75 cm.

Sorry, I wasn't online. I couldn't immediately answer you.

[DQW]

No immediate thoughts on how that came about. But as I said, I know very little about strobes, so perhaps I should read up something about how they work. I'll do that, if I find some time tomorrow. It's late now.

 

Here's my thinking. The LCM of 1/6 and 1/8 is 1/2. This means that every 1/2 second, (or at every third frame) the phase of the wave will be the same. So, I guessed that the apparent period is 1/2 second or the apparent frequency is 2 Hz. This gave me a wavelength of 6cm.

[swansont]

If a wave with wavelength 1.5 cm and frequency 8Hz' date=' is viewed through a stroboscope with 6Hz, what's the change of its wavelength?

My answer is not identical to what in my text book.

My thought is :there is no change of the wavelength, as the time given is enough for the wave to move over one wavelength.[/quote']

 

I don't fully understand what they are asking. The wavelength measurement doesn't change if you can see two peaks, it's just that the wave will appear to move at a different speed - if the strobe were at 8 Hz the wave would appear stationary.

[DQW]

Oh, I'd imagined that you can only see one "point" on the wave in each frame (ie : that in each frame at time t=t' you can see all values of y(t') ).

[Primarygun]

I don't fully understand what they are asking. The wavelength measurement doesn't change if you can see two peaks, it's just that the wave will appear to move at a different speed - if the strobe were at 8 Hz the wave would appear stationary.

I'd think reduction of apparent wavelength merely occurs when the stroboscope frequency is higher than the wave frequency. When the case is vice versa, this one illustrates as an example, I'd think the apparent wavelength is still 1.5cm.

However, Boris did find 0.75cm as the answer, but he said he is weak in illustrating the solution.