How Is Tension Calculated in a Harpsichord String?

[kbyws37]

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

 

[OlderDan]

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

 

[kbyws37]

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.

 

[OlderDan]

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