(II) A guitar string produces 3 beats /s when sounded witha 350-Hz tuning fork and 8 beats/s when sounded with a355-Hz tuning fork. What is the vibrational frequency of thestring? Explain your reasoning.

(3) A harmonica makes sounds when a reed inside of it vibrates back and forth. We can consider this to the same as a string with mass 16.5g that is fixed at both ends. The reed is experiencing 639N of tension. (a) This particular harmonica is in the key of D# and it can emit as a fundamental frequency f = 311.13H z. What is the length of the reed? (b) What is the n = (c) A person decides to produce the fundamental frequency on the harmonica in a room 20°C while rolling around in their favorite chair at 8.19m/s. They hear the echo of their playing off the wall that they are moving away from. What is the frequency of the echo heard by the harmonica player? (d) When an observer is 6.79m away from the harmonica player, the sound intensity level is 86.6dB. What is the sound intensity level of the music when the observer is 41.6m away from the harmonica player? 3 harmonic for this reed? at T

(I) A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)

(II) A tight guitar string has a frequency of 540 Hz as itsthird harmonic. What will be its fundamental frequency ifit is fingered at a length of only 70% of its original length?

(II) A guitar string is 92 cm long and has a mass of 3.4 g.The distance from the bridge to the support post is l= 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?

(II) Two violin strings are tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.5%. What will be the beat frequency heard when the two strings are played together?

(3) The lowest note on a piano (the first harmonic vibration) is the "A" note, which has a frequency of 27.5 Hz. The entire string is 2.0 m long and has a mass of 402 g. The vibrating section of the string is 1.89 m long. (a) What tension is required to tune the string properly? (answer: 2170 N) (b) What is the wavelength of the first harmonic vibration? (answer: 3.78 m) (c) What are the wavelength and frequency of the second harmonic vibration of the string? (answer: 55.0 Hz and 1.89 m) (d) What are the wavelength and frequency of the fourth harmonic vibration of the string? (answer: 110 Hz and 0.945 m) 2L F fn = 2L n

(I) What would you estimate for the length of a bass clarinet,assuming that it is modeled as a closed tube and that thelowest note that it can play is a Db whose frequency is 69 Hz?

(ii) Explain the physical phenomenon occurring at the junction of two different strings of different materials but same diameter attached to each other when a harmonic wave is being propagated in the hybrid string.