Question

A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 36.1 vibrations in 33.5 seconds. Also a given maximum travels 425 cm along the rope in 9.4s. What is the wavelength? Answer in units of cm

Answer 1

Wavelength = 41.94 cm

Step-by-step explanation:

Given:

Number of vibrations (N) = 36.1

Time taken (t) = 33.5 s

Distance traveled by wave (D) = 425 cm

Time taken by the wave to travel the distance (T) = 9.4 s

Now, we know that,

Frequency = Number of vibrations per second

So, frequency of the wave is given as:

`f=(N)/(t)=(36.1)/(33.5\ s)=1.078\ s^(-1)`

Now, speed of the wave is given as the ratio of distance traveled by time taken for the travel. So,

Speed of wave is,
`v=(D)/(T)=(425\ cm)/(9.4\ s)=45.213\ cm/s`

Now, from wavelength equation, we have:

Speed = Frequency × Wavelength.

Rewriting in terms of wavelength, we get:

`Wavelength(\lambda)=(Speed)/(Frequency)\\\\\lambda=(v)/(f)=(45.213\ cm/s)/(1.078\ s^(-1))=41.94\ cm`

Therefore, the wavelength of the wave is 41.94 cm.