The speed of a transverse wave on a stretched string can be changed by adjusting the tension of
the string. A stationary wave pattern is set up on a stretched string using an oscillator set at a
frequency of 650 Hz.
How must the wave be changed to maintain the same stationary wave pattern if the applied
frequency is increased to 750 Hz?
How must the wave be changed? Do you meant tension be changed?
f=sqrt(tension)
750/650 = sqrt(T)
T=1.331 so the tension must be increased 33 percent.
To maintain the same stationary wave pattern on a stretched string when the applied frequency is increased, you need to adjust the tension of the string.
The speed of a wave on a stretched string is given by the equation:
v = √(F/μ)
where:
v is the speed of the wave,
F is the tension in the string, and
μ is the linear density of the string.
Since we want to maintain the same stationary wave pattern, the speed of the wave must remain constant. Therefore, we can set up the equation:
v1 = v2
√(F1/μ) = √(F2/μ)
To solve for F2 (the new tension), we need to know the linear density of the string, which is not given in the question. Linear density is typically given in units of mass per unit length (kg/m or g/cm).
Once you have the linear density of the string, you can rearrange the equation and solve for F2:
F2 = (v2^2) * μ
where:
v2 is the new speed of the wave, which can be determined using the equation:
v2 = λ * f2
where:
λ is the wavelength of the wave, and
f2 is the new frequency.
Since only the frequency is given in the question, and not the wavelength or linear density, you would first need to find the wavelength of the wave at the new frequency using the equation:
v = λ * f
where v is the initial speed of the wave (which can be calculated using the given frequency of 650 Hz and the linear density), λ is the initial wavelength, and f is the initial frequency.
Once you have the new wavelength for the frequency of 750 Hz, you can use it along with the new frequency and the initial linear density in the equation to calculate the new tension of the string.