A long string is pulled so that the tension in it increases by a factor of four. If the change in length is negligible, by what factor does the wave speed change?Select one:a.0.50b.2.0c.0.25d.4.0
Question
A long string is pulled so that the tension in it increases by a factor of four. If the change in length is negligible, by what factor does the wave speed change?Select one:a.0.50b.2.0c.0.25d.4.0
Solution
The speed of a wave in a string under tension is given by the formula v = sqrt(T/μ), where T is the tension in the string and μ is the linear mass density (mass per unit length).
If the tension in the string is increased by a factor of four, the new wave speed v' is given by v' = sqrt(4T/μ).
Since the square root of 4 is 2, the wave speed increases by a factor of 2.
So, the correct answer is b. 2.0.
Similar Questions
If the tension in a length of string is doubled, the wavelength of standing waves in the string changes by what factor?Select one:a.1/√2b.1/2c.1d.2e.√2
If the tension in a guitar string is increased fourfold without changing its mass or length, how will the speed of the wave on the string change?Select one:a.It will remain the sameb.It will quadruplec.It will halved.It will double
Transverse waves with a speed of 46.5 m/s are to be produced on a stretched string. A 4.30-m length of string with a total mass of 0.0600 kg is used.(a) What is the required tension in the string? N(b) Calculate the wave speed in the string if the tension is 8.00 N. m/s
The speed of a wave on a string is 150m/s when the tension is 120N. The percentage increase in the tension in order to raise the wave speed by 20% is?
Calculate the speed of a wave travelling along a stretched string that is under a tension of50 N and has a mass per unit length of 3.110–4 kg m–1
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.