To solve this problem, we will apply the concepts related to the kinematic equations of linear motion, which define speed as the distance traveled per unit of time. Subsequently, the wavelength is defined as the speed of a body at the rate of change of its frequency. Our values are given as,
[tex]\text{Length of the string} = L = 4.32 m[/tex]
[tex]\text{Frequency of the wave} = f = 75 Hz[/tex]
[tex]\text{Time taken to reach the other end} = t = 0.5 s[/tex]
Velocity of the wave,
[tex]V = \frac{L}{t}[/tex]
[tex]V = \frac{4.32 m}{0.5s}[/tex]
[tex]V = 8.64m/s[/tex]
Wavelength of the wave,
[tex]\lambda = \frac{V}{f}[/tex]
[tex]\lambda = \frac{8.64m/s}{75Hz}[/tex]
[tex]\lambda = 0.1152m[/tex]
[tex]\lambda = 11.52cm[/tex]
Therefore the wavelength of the waves on the string is 11.53 cm
11.52cm
The velocity, v, of a wave undergoing a simple harmonic motion is related to the wavelength, λ, and frequency, f, of the wave as follows;
v = f x λ -----------------(i)
But;
The velocity is also given as the ratio of the length, l, of the body producing the wave to the time taken, t, to undergo the motion. i.e
v = [tex]\frac{l}{t}[/tex] --------------(ii)
Now, substitute the value of v in equation (ii) into equation (i) as follows;
[tex]\frac{l}{t}[/tex] = f x λ ----------------(iii)
From the question,
l = 4.32m
t = 0.5s
f = 75Hz
Substitute these values into equation (iii) as follows;
[tex]\frac{4.32}{0.5}[/tex] = 75 x λ
Make λ subject of the formula;
λ = [tex]\frac{4.32}{0.5*75}[/tex]
λ = 0.1152m
Convert the value to cm by multiplying by 100
λ = 0.1152 x 100cm = 11.52cm
Therefore, the wavelength of the waves on the string is 11.52cm
