A long rope is fixed at one end, and the free end is made to oscillate in one plane at right angle with a frequency of 4Hz. The successive crest are 0.6cm apart. Calculate the speed of the wave. For what frequency will the wave length be 30cm?
period T = 0.25 second
goes 0.6 cm in 0.25 seconds
distance = speed * time
.6 cm = v * 0.25
so v = 2.4 cm/s = 0.024 m/s
Do the second part the same way. Remember frequency = 1 / period
To calculate the speed of the wave in the given scenario, we can use the formula:
v = λ * f
Where:
v = speed of the wave
λ = wavelength
f = frequency
Given that the successive crests are 0.6 cm apart, we can determine the wavelength by multiplying the distance between the crests by 2 (since one full wave consists of one crest and one trough):
λ = 2 * 0.6 cm
λ = 1.2 cm
Now, we know the frequency is 4 Hz and the wavelength is 1.2 cm. We can substitute these values into the formula to calculate the speed of the wave:
v = 1.2 cm * 4 Hz
v = 4.8 cm/s
Therefore, the speed of the wave is 4.8 cm/s.
To find the frequency at which the wavelength will be 30 cm, we can rearrange the formula for wavelength, λ, to solve for frequency, f:
f = v / λ
Given that the wavelength, λ, is 30 cm and the speed, v, is 4.8 cm/s, we substitute these values into the formula:
f = 4.8 cm/s / 30 cm
f = 0.16 Hz
Therefore, the frequency at which the wavelength will be 30 cm is 0.16 Hz.
To calculate the speed of the wave, we need to use the formula v = f * λ, where v is the wave speed, f is the frequency, and λ is the wavelength.
In this case, the frequency (f) is given as 4 Hz and the successive crests are 0.6 cm apart. We can convert the distance between successive crests to the wavelength (λ) by dividing it by the number of crests:
λ = distance between crests / number of crests
The number of crests in this case can be calculated by dividing the oscillation frequency (f) by the number of complete oscillations in one second, which is equal to the frequency itself:
number of crests = f
Substituting the given values, we have:
λ = 0.6 cm / 4 crests
λ = 0.15 cm/crest
Now, we can find the wave speed (v) by multiplying the frequency (f) by the wavelength (λ):
v = f * λ
v = 4 Hz * 0.15 cm/crest
v = 0.6 cm/s
Therefore, the speed of the wave is 0.6 cm/s.
Now, let's calculate the frequency required for a wavelength of 30 cm using the same formula.
The wavelength (λ) is given as 30 cm, and we need to find the frequency (f). Rearranging the formula, we have:
f = v / λ
Substituting the given values, we have:
f = 0.6 cm/s / 30 cm
f = 0.02 Hz
Therefore, the required frequency for a wavelength of 30 cm is 0.02 Hz.