A string fixed at both ends is 9.31 m long and has a mass of 0.125 kg. It is subjected to a tension of 100.0 N and set oscillating.
(a) What is the speed of the waves on the string?
m/s
(b) What is the longest possible wavelength for a standing wave?
m
(c) Give the frequency of that wave.
Hz
wave velocity=sqrt (tension/(mass/length)
longest wavelength: 1/2 Lambda = 9.31 m long
frequency=speedofwave/wevelength
he equation of a transverse wave on a string is
y = (4.8 mm) sin[(14 m-1)x + (440 s-1)t]
The tension in the string is 10 N. (a) What is the wave speed? (b) Find the linear density of this string.
To find the speed of the waves on the string, we can use the formula:
wave speed (v) = (tension (T) / linear mass density (μ))^0.5
First, we need to find the linear mass density, which is defined as the mass per unit length. We can calculate it using the formula:
linear mass density (μ) = mass (m) / length (L)
Given:
Length of the string (L) = 9.31 m
Mass of the string (m) = 0.125 kg
Tension (T) = 100.0 N
(a) The speed of the waves on the string:
linear mass density (μ) = 0.125 kg / 9.31 m = 0.01343 kg/m
v = (100.0 N / 0.01343 kg/m)^0.5 ≈ 79.617 m/s
Therefore, the speed of the waves on the string is approximately 79.617 m/s.
(b) To find the longest possible wavelength for a standing wave, we use the formula:
λ = 2L
where λ is the wavelength and L is the length of the string.
λ = 2 * 9.31 m = 18.62 m
Therefore, the longest possible wavelength for a standing wave is 18.62 m.
(c) The frequency of the wave can be determined using the formula:
f = v / λ
where f is the frequency, v is the speed of the wave, and λ is the wavelength.
f = 79.617 m/s / 18.62 m ≈ 4.28 Hz
Therefore, the frequency of the wave is approximately 4.28 Hz.
To find the speed of the waves on the string, we can use the formula:
v = √(T/μ),
where:
v is the velocity of the waves on the string,
T is the tension in the string,
and μ is the linear mass density of the string.
(a) To calculate the speed of the waves on the string, we need to find the linear mass density first. Linear mass density (μ) is defined as the mass per unit length.
μ = m / L,
where:
m is the mass of the string, and
L is the length of the string.
Given:
Mass of the string (m) = 0.125 kg,
Length of the string (L) = 9.31 m.
Substituting the values into the formula:
μ = 0.125 kg / 9.31 m.
Now, we can substitute the value of μ and the tension given in the formula for v:
v = √(100.0 N / (0.125 kg / 9.31 m)).
Calculating the value of v will give us the speed of the waves on the string in meters per second (m/s).
(b) The longest possible wavelength for a standing wave on a string is twice the length of the string. Therefore, the longest possible wavelength λ is given by:
λ = 2L.
Given:
Length of the string (L) = 9.31 m.
Substituting the value of L into the formula:
λ = 2 * 9.31 m.
Calculating the value of λ will give us the longest possible wavelength in meters (m).
(c) The frequency of the longest possible standing wave can be calculated using the formula:
f = v / λ,
where:
f is the frequency,
v is the velocity of the waves on the string,
and λ is the wavelength.
Substituting the values of v and λ given in parts (a) and (b) respectively:
f = v / (2 * L).
Calculating the value of f will give us the frequency in Hertz (Hz).