How Is Tension Calculated in a Harpsichord String?

In summary: Now we can plug this into the equation:v = square root of (F / (m/L))1440 = square root of (F / (.000025))1440^2 = F / (.000025)F = 1440^2 * .000025F = 51840000 * .000025F = 1296 NSo the tension in the string is 1296 N.
  • #1
kbyws37
67
0
A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450 Hz.

(a) What is the speed of the transverse string waves?
I did 450 x 2(1.60) = 1440 m/s which is correct.

(b) It asks for the tension.
I tried it but am not getting the right answer.
I used
v = square root of (F / (m/L)) where v = 450 Hz, and m/L is 25000 kg/m
So 1440 = squre root of (F/25000)
F = 82.8 N which is incorrect.
Not sure what I am doing wrong.

Thanks
 
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  • #2
kbyws37 said:
A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450 Hz.

(a) What is the speed of the transverse string waves?
I did 450 x 2(1.60) = 1440 m/s which is correct.

(b) It asks for the tension.
I tried it but am not getting the right answer.
I used
v = square root of (F / (m/L)) where v = 450 Hz, and m/L is 25000 kg/m
So 1440 = squre root of (F/25000)
F = 82.8 N which is incorrect.
Not sure what I am doing wrong.

Thanks

450 Hz is a frequency, not a velocity, but it looks like you did in fact calculate the velocity correctly. 25mg/m is not 25000 kg/m
 
  • #3
Oops, I meant to say that v = 1440.
So for this equation,
v = square root of (F / (m/L))

I know v and I am looking for F. But I am having trouble converting
25 mg/m to m/L.
 
  • #4
kbyws37 said:
Oops, I meant to say that v = 1440.
So for this equation,
v = square root of (F / (m/L))

I know v and I am looking for F. But I am having trouble converting
25 mg/m to m/L.

1 mg = 1/1000 g
1 g = 1/1000 kg

All unit conversions involve multiplying by one. There are endless ways to write one, such as

1 = 1000mg/g = 1g/1000mg
1 = 1000g/kg = 1kg/1000g

μ = 25mg/m*1*1*1*1*1*1*1*1*1*1*1 = 25mg/m
μ = 25mg/m(1g/1000mg)(1kg/1000g) is still 25mg/m, but the units divide out to give

μ = 25mg/m(1g/1000mg)(1kg/1000g) = .000025 kg/m
 

Related to How Is Tension Calculated in a Harpsichord String?

1. What causes tension in harpsichord strings?

Tension in harpsichord strings is caused by the weight of the strings and the force applied by the tuning pins to keep the strings at the desired pitch.

2. How is the tension of harpsichord strings measured?

The tension of harpsichord strings is typically measured in pounds or kilograms using a tension gauge, which is a specialized tool designed to measure the tension of strings.

3. Can the tension of harpsichord strings be adjusted?

Yes, the tension of harpsichord strings can be adjusted by tightening or loosening the tuning pins. This will change the pitch of the strings and the overall tension in the instrument.

4. What effect does tension have on the sound of a harpsichord?

The tension of harpsichord strings directly affects the sound and tone of the instrument. Higher tension strings produce a brighter and louder sound, while lower tension strings produce a softer and more mellow sound.

5. Are there any risks associated with changing the tension of harpsichord strings?

Changing the tension of harpsichord strings should only be done by a trained professional, as it can potentially damage the instrument if not done properly. It is important to follow proper techniques and precautions when adjusting the tension of harpsichord strings.

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