Question

Standing Waves!

Questions: I. You have a fundamental standing wave at a frequency f, tension F, linear density μ and length L. What tension would you use to double the frequency? 2. You have a fundamental standing wave at a frequency f, tension F, linear density μ and length L. What length would you use to double the frequency? 3. You have a fundamental standing wave at a frequency f, tension F, linear density μ and length L. What linear density would you use to double the frequency? 4. You have a fundamental standing wave at a frequency of 500 Hz, tension F, linear density μ and length L. What would the new fundamental frequency be if you doubled the tension, and at the same time cut the length in half and cut the linear density in half?

Answer 1

WE know that

$f=\frac{\sqrt{F/\mu}}{2L}$

of this form only,

1.

if we want to double the frequency, then we have to make the tension 4 times i.e 4F.

2

Cutting the length in half would double the frequency i.e L/2

3.

If we make the liner mass density to be 1/4 of original it will double the frequency.

4.

$f=2\frac{\sqrt{4F/\mu}}{2L}$

So, it will be 4 times of the original value,

so new frequency will be,

f=4*500

=2000Hz