Question

The following four waves are sent along strings with the same linear densities (x is in meters and t is in seconds). Rank the waves according to the tension in the strings along which they travel, greatest first:

(1) y1=(3 mm)sin(x3t)y_1 = (3 \text{~mm}) \sin(x - 3t), (2) y2=(6 mm)sin(2xt)y_2 = (6 \text{~mm}) \sin(2x - t),

(3) y3=(1 mm)sin(4xt)y_3 = (1 \text{~mm}) \sin(4x - t), (4) y4=(2 mm)sin(x2t)y_4 = (2 \text{~mm}) \sin(x - 2t)

Solution

Verified
Answered 4 months ago
Answered 4 months ago
Step 1
1 of 5

Introduction

Knowing the four waves, precisely their unique mathematical forms, which we can observe below,

y1(x,t)=(3 mm)sin(x3t)y2(x,t)=(6 mm)sin(2xt)y3(x,t)=(1 mm)sin(4xt)y4(x,t)=(2 mm)sin(x2t) \diamond \quad y_1(x,t)=(3~\mathrm{mm})\cdot\sin{(x-3\cdot t)}\\[5pt] \diamond \quad y_2(x,t)=(6~\mathrm{mm})\cdot\sin{(2\cdot x-t)}\\[5pt] \diamond \quad y_3(x,t)=(1~\mathrm{mm})\cdot\sin{(4\cdot x-t)}\\[5pt] \diamond \quad y_4(x,t)=(2~\mathrm{mm})\cdot\sin{(x-2\cdot t)}\\[5pt]

and the fact that the linear densities μ\mu of the strings along which they travel are identical, we need to rank them with respect to the corresponding values of the tension τ\tau in the strings.

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Related questions