Question

What happens to the standing wave frequencies if you quadruple the tension in the string?

What happens to the frequencies if you quadruple the mass per unit length of the string?
Pleasee help meee!!

Answer 1

Quadrupling the tension in a string results in an increase in the frequency of standing waves, while quadrupling the mass per unit length results in a decrease in the frequency.

Step-by-step explanation:

When you quadruple the tension in a string, the frequency of standing waves will increase. This is because the wave speed on a string is determined by the tension (T) and the linear mass density (μ) according to the formula v = √(T/μ). When tension increases, wave speed increases, and since frequency (f) is related to speed (v) and wavelength (λ) by the formula f = v/λ, and the wavelength is fixed by the length of the string and its endpoints, the frequency will increase as the tension increases.

If you quadruple the mass per unit length of the string (μ), the frequency of the standing waves will decrease. This effect stems from the inverse relationship between the linear mass density and wave speed in the equation v = √(T/μ). With an increase in μ, the wave speed decreases. As the wave speed decreases and the wavelength remains constant (due to the length of the string and fixed endpoints), the frequency, which is directly proportional to the wave speed, will also decrease.

Answer 2

. A standing wave on a string (fixed at both ends) has a fundamental frequency f. If you quadruple the tension in the string, how can you change the length of the string so that the fundamental frequency remains the same? ... double the length.