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(30) A stretched string of length L is observed to vibrate in six equal segments

ID: 2255554 • Letter: #

Question

(30) A stretched string of length L is observed to vibrate in six equal segments when driven by a 725-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in two segments? answer in Hz

(29)How far, and in what direction, should a cellist move her finger to adjust a string's tone from an out-of-tune 447 Hz to an in-tune 440 Hz? The string is 68.0 cm long, and the finger is 17.9 cm from the nut for the 447-Hz tone. (Indicate the direction with the sign of your answer. Take the direction towards the nut to be positive.)
     cm

     N


A stretched string of length L is observed to vibrate in six equal segments when driven by a 725-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in two segments? answer in Hz How far, and in what direction, should a cellist move her finger to adjust a string's tone from an out-of-tune 447 Hz to an in-tune 440 Hz? The string is 68.0 cm long, and the finger is 17.9 cm from the nut for the 447-Hz tone. (Indicate the direction with the sign of your answer. Take the direction towards the nut to be positive.)A steel wire in a piano has a length of 0.5000 m and a mass of 3.700 times 10-3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC = 261.6 Hz on the chromatic musical scale)?

Explanation / Answer

30)

since velocity in string remains same coz tension remains same

?1xf1=f2x?2

?1=2L/5

?2=L

f1=725

we get f2=290 Hz

29)

Use the formula v = f?

The velocity for bot notes will be the same so we can set up a proportionality

f1?1 = f2?2

The wavelength will be twice the string vibrating length

The string vibrating length is .68 - .179 = .501, so the wavelength is 1.002 m

(447)(1.002) = (440)(?2)

?2 = 1.01794 m

String length of vibration must be .50897 cm

Since the total string lenght is .68, then .68 - .50897 = .17103 m or 17.103 cm

Since her finger is 18.6 cm from the nut, she needs to move her finger toward the nut. The distance is

18.6 - 17.103 = 1.497 cm

28)

f = n v / 2 L

v = ?T/?

? = 3.7 x 10-3 / 0.5

= 7.4 x10-3

261.6 = 1 x ?(T/ 7.4 x10-3) / 2 x 0.5

T = 506.415 N