A 48-cm-long wire with a mass of 11.0 g is under a tension of 50.5 N. Both ends of the wire are held rigidly while it is plucked.

(a) What is the speed of the waves on the wire?
(b) What is the fundamental frequency of the standing wave?

The answers are 50.5 m/s and 48.9 Hz respectively. How do I get these answers?

For part (a) I've been doing the following work:

u=M/L; where u= mass per unit length
u=(0.011)/(.48)= 0.022916667

v= sqrt(T/u); where T = tension
v= sqrt(50.5/0.022916667) = 47.0 m/s

I'm not really sure how to figure out part (b); however, I'm sure that it's answer relies on me figure out part (a) correctly.

Your answer for part A is correct.

Velocity in the stretched string is
v = sqrt(T/m(o)).
=sqrt(50.5•0.48/0.011)=46.94 m/s

Part B

Part B
λ =2 L= 0.96 m.
λ =v/f,
f=v/ λ =46.94/0.96=48.9 m

Thank you. I guess WebAssign made a mistake.

Also, shouldn't f=48.9 m be f=48.9 Hz?

Certainly, Hz

To find the speed of the waves on the wire, you can use the formula:

speed = sqrt(tension / (mass / length))

(a) Speed of the waves on the wire:
- Tension (T) = 50.5 N
- Mass (m) = 11.0 g = 0.011 kg
- Length (L) = 48 cm = 0.48 m

Substituting the values into the formula:

speed = sqrt(50.5 N / (0.011 kg / 0.48 m)) = 50.5 m/s

So, the speed of the waves on the wire is 50.5 m/s.

To find the fundamental frequency of the standing wave on the wire, you can use the formula:

fundamental frequency = (speed / (2 * length))

(b) Fundamental frequency of the standing wave:
- Speed (v) = 50.5 m/s
- Length (L) = 0.48 m

Substituting the values into the formula:

fundamental frequency = (50.5 m/s / (2 * 0.48 m)) = 52.7 Hz

So, the fundamental frequency of the standing wave is 52.7 Hz.

It seems the answers you have provided (50.5 m/s and 48.9 Hz) may be incorrect. Double-check your calculations or the given values to ensure accurate results.