Question

A thin, 71.0-cm wire has a mass of 16.3 g . One end is tied to a nail, and the other end is attached to a screw that can be adjusted to vary the tension in the wire.
(a) To what tension in Newtons must you adjust the screw to that a transverse wave of wavelength 3.33 cm makes 875 vibrations per second?
(b) How fast would this wave travel?

Answer 1

Answer:

(a) Tension=28.28 N

(b) Speed=29.14 m/s

Explanation:

Given data

f(frequency)=875 vibration/second

λ(wave length)=3.33 cm=0.0333 m

m(mass)=16.3 g=0.0163 kg

To find

(a) Tension

(b) Speed

Solution

For (b) at what speed the wave travel

$V_{speed}=f_{frequency}*l_{wave-length}\\V_{speed}=(875)*(0.0333)\\ V_{speed}=29.14m/s$

For (a) Tension

$V_{speed}=\sqrt{\frac{T_{tension}}{l_{wave-length}} }\\ T_{tension}=l_{wave-length}*(V_{speed})^{2}\\ T_{tension}=(0.0333m)*(29.14m/s)^{2}\\ T_{tension}=28.28N$

So screw must adjust such that tension in the wire is 28.28 N