Question

What is the relationship between wave frequency and period? If the frequency of a wave doubles, what happens to its period? If the period doubles, what happens to the frequency?What are beats? How are beats related to frequency? A piano tuner hears three beats per second when a tuning fork and a note are sounded together and six beats per second after the string is tightened. What should the tuner do next, tighten or loosen the string? Explain your answer.What is resonance and the conditions for resonance? How is it related to frequency? Give examples.Finally, what is the Doppler effect and how is it related to frequency?

Answer 1

Relationship between frequency and period is as follows: Here, f is the frequency and T is the time period. Since frequency and time period are inversely proportional hence, if you doulble the frequency then time period will be halved. If time period will be doubled then the frequency will halved. When two waves of different freqncy then approach to the ear then they interefer and produce constructive and distructive intereference. When constructive interference is heard by the ear then sound appears loud and when distructive interference is heard then the sound appears soft. This phenomenon of alternatively softness and loudness is known as beat. The relation between beats and frequency is as follows: Fbeat = |fz - fil Here, feat is the frequency of the beat and fe, f, are freqneies of the waves. According to the above definition beat frequency depends on the difference in freqncies. If difference f-f, will decrease then beat frequency will decrease. To match the freqnecy of the fork and the piano, beat freqnecy should be minimum or zero. Now, consider the situation. Initial beats were 3, on tightening beats increases to 6 means deference in freqneyc of piano and fork increases. To decrease the difference, tunner must loose then string. When two waves of same frequency and phase differecn meet at a point then interefer each other this interference is known as resonance. For resonance, frequency and phase differenc of the two waves should be same.