Frequency and Tension in Waves on a String
a) How could you increase the tension, T, in the string in the lab?
Option A: Adjust the force applied to the ends of the string.
b) Suppose that the frequency stays the same, explain what would happen (and why) to each of the remaining variables (v, A, pi, and T0) as a result of an increase in tension?
Option A: Wave velocity (v) remains unchanged since tension stays constant. Amplitude (A) remains unaffected too. Time period (T0) decreases as it is inversely proportional to frequency.
c) How could you increase the frequency, f, of the waves on the string in the lab?
Option A: Adjust the frequency of the source producing the waves.
d) Suppose that the tension, T, stays the same, explain what would happen (and why) to each of the remaining variables (v, A, pi, and T0) as a result of this increase in frequency?
Option A: Wavelength (λ) decreases as it is inversely proportional to frequency. Wave velocity (v) and amplitude (A) remain constant. Time period (T0) decreases as it is inversely proportional to frequency.
Answer:
To increase the tension, T, in the string in the lab, one can adjust the force applied to the ends of the string. This can be done by using weights or applying a greater pulling force. To increase the frequency, f, of the waves on the string in the lab, one can adjust the frequency of the source producing the waves. If the tension, T, stays the same while increasing the frequency, several variables in the wave equation are affected.
An increase in frequency would lead to a decrease in wavelength (λ) since they are inversely proportional. The wave velocity (v) would remain unchanged since the tension remains constant. The amplitude (A) of the wave would also remain unaffected. The time period (T0) of the wave, on the other hand, would decrease since T0 is inversely proportional to the frequency.
In summary, increasing tension involves adjusting the force on the string, increasing tension affects wave velocity and time period while leaving amplitude and wavelength unchanged, increasing frequency involves adjusting the frequency of the source, and increasing frequency affects wavelength and time period while leaving wave velocity and amplitude unchanged.