My LO6

1. ArthurTse
20453149
Guitar Strings
A guitarstringis a type of string where bothendsof the stringare claspedtightly.Thiscreatesaperfect
environmentforstandingwavestoform.The wave speedona particularguitarstringis500 m/s.The
lengthof thisguitarstring is 65 cm.
a) Findthe fundamental frequency.
b) Findthe secondharmonic.
c) Findthe thirdharmonic.
Solution:
a) Since the fundamental frequencyisjustwhenthe stringhasnoantinodesotherthanthe endsof the
string,thenthe wavelengthwill be twicethe length.
The wavelengthforthe fundamental frequency: 𝜆 = 2𝐿
The wave speedformula: 𝑣 = 𝜆𝑓
Combine themandthisformulaiscreated:
𝑣 = 2𝐿𝑓
Solve forf:
𝑓 =
𝑣
2𝐿
Pluginthe values:
𝑓 =
(500)
2(0.65)
𝑓 = 384.6 𝐻𝑧
b) Followingthe same scheme asparta),this time use the wavelengthforthe secondharmonicwhichis:
𝜆 = 𝐿
Thisis because there isone antinode rightinthe middleof the lengthof string.
Thenthe wave speedformulabecomes:
𝑣 = 𝐿𝑓
Solve forf:
𝑓 =
𝑣
𝐿
Pluginthe values:
𝑓 =
(500)
(0.65)
𝑓 = 765.2 𝐻𝑧
c) Wavelengthforthe thirdharmonicis:
𝜆 =
2
3
𝐿
Therefore the wave speedformula:
𝑣 =
2
3
𝐿𝑓
Solve forf:
𝑓 =
3𝑣
2𝐿
Pluginthe values:
𝑓 =
3(500)
2(0.65)
𝑓 = 1153.8 𝐻𝑧