Question

1. a string of mass m is under tension, and the speed of a wave in the string is v. what will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension? a. 4v b. \\( \frac { v } { 2 } \\) c. \\( \frac { v } { \sqrt { 2 } } \\) d. \\( v \sqrt { 2 } \\) 11. figure below is a \snapshot\ of a wave at a given time. the frequency of the wave is 120 hz. what is the wave speed? a. 12 m/s b. 24 m/s c. 36 m/s d. 48 m/s

Explanation:

Question 10

Step1: Recall wave - speed formula

The speed of a wave on a string is \(v = \sqrt{\frac{T}{\mu}}\), where \(T\) is tension and \(\mu=\frac{m}{L}\) (mass per unit length). Initially, \(\mu_1=\frac{m}{L}\), so \(v = \sqrt{\frac{TL}{m}}\).

Step2: Calculate new mass per unit length

When mass is \(2m\) (length \(L\) unchanged), \(\mu_2=\frac{2m}{L}\). The new speed \(v_2=\sqrt{\frac{TL}{2m}}\).

Step3: Relate new and old speeds

Since \(v = \sqrt{\frac{TL}{m}}\), then \(v_2=\frac{v}{\sqrt{2}}\)

Step1: Find wavelength from graph

From the \(x - y\) graph (wave snapshot), the wavelength \(\lambda\) is the distance between two consecutive crests (or troughs). Here, \(\lambda = 0.2m\)

Step2: Use wave - speed formula

The wave - speed formula is \(v = f\lambda\), where \(f = 120Hz\) and \(\lambda=0.2m\)
Substitute values: \(v=120\times0.2\)

Step3: Calculate the speed

\(v = 24m/s\)

Answer:

C. \(\frac{v}{\sqrt{2}}\)

Question 11