Problem 2: On a violin, the string with the smallest linear density (0.00042 kg/m) is the E5 string. The string produces a fundamental frequency (n = 1) of 659.3 Hz and has a length of 0.32 m between the two fixed ends. What is the tension in the string?
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- A piano has the widest range of notes of any instrument. It achieves this large range using both the length and mass density, H, of the strings. In a real piano, most of the strings have roughly the same tension. We shall assume that all the strings in our piano have a tension of T = 760 Newtons. L1 L1 is the longest string L88 is the shortest string L27 Bass strings L26 Line of strike Treble strings L88 Grand Piano Details Grand Piano Simplified We shall assume the following regarding the longest and shortest strings in the piano: String frequency (Hz) length (m) tension (N) L1 27.5 0.163 760 L88 4186.01 0.046 760 Calculate all the following: The linear mass density of the L1 string: µ1 = kg/m %3D The linear mass density of the L88 string: µ88 = kg/m As you likely calculated, the L1 string has a much higher u than the L88 string. If you have ever looked inside a piano you know this to be true. For the next calculation we are going to do something silly. We will calculate how long a…The approach to solving this problem is similar to that taken in Multiple-Concept Example 4. On a cello, the string with the largest linear density (2.16 x 10-3 kg/m) is the C string. This string produces a fundamental frequency of 71.3 Hz and has a length of 0.927 m between the two fixed ends. Find the tension in the string.A guitar player can change the frequency of a string by “bending” it—pushing it along a fret that is perpendicular to its length. This stretches the string,increasing its tension and its frequency. The G string on a guitar is 64 cm long and has a tension of 74 N. The guitarist pushes this string down against a fret located at the center of the string, which gives it a frequency of 392 Hz. He then bends the string, pushing with a force of 4.0 N so that it moves 8.0 mm along the fret. What is the new frequency?
- Biologists think some spiders “tune” strands of their web to give enhanced response at frequencies corresponding to those at which prey might struggle. Orb spider silk has a typical diameter of 20 µm, and spider silk has a density of 1300 kg/m3. To have a fundamental frequency at 100 Hz, to what tension must a spider adjust a 12 cm long strand of silk?In your summer job as a piano tuner, you notice that the A-note above middle C sounds a little flat. Ideally this note should have a fundamental frequency of exactly 440.0 Hz, but playing it yields a 433.0 Hz tone with its current tension of 1200 N. What new tension do you need for the string to have the proper sound?A 38.0-Hz sound wave is barely audible at a sound intensity level of 60.0 dB. The density of air at 20.0°C is 1.20 kg/m3. Speed of sound in air at 20.0°C is 343 m/s. What is the displacement amplitude of a 38.0-Hz sound wave? What is the ratio of the displacement amplitude to the average distance between molecules in air at room temperature, about 3.00 nm?
- A simple instrument with two strings S1 and S2 is shown in the figure. Both strings have the same tension T and length L, but the strings have different masses to play two different notes. In its fundamental mode, string S1 has a mass of 4.43 g and its fundamental frequency f1 = 263 Hz (the musical note middle C). What is the fundamental frequency of string S2 if it has a mass m = 8.98 g? Give your answer in units of Hz.?3. One type of steel has a density of 7.8 x 103 kg and a breaking stress of m3 N 7.0 x 108 ,. A cylindrical guitar string is to be made of 4.0g of this steel. (a) What m2 are the length and radius of the longest and thinnest string that can be placed under a tension of 900 N without breaking? (b) What is the highest fundamental frequency that this string could have?
- In complex tones (that are composed of many harmonics), the perceived pitch usually corresponds to the pitch of the fundamental frequency (the lowest frequency in the harmonic series). The set of harmonics can sound like the pitch of the fundamental even when the fundamental is not physically present (the case of the missing fundamental). For each harmonic series, what single frequency should have the same perceived pitch? a. 1000 + 2000 + 3000 + 4000hz = ? b. 2000 + 3000 + 4000 + 5000hz = ? c. 1000 + 1500hz = ? d. 2000 + 2500 + 3000hz = ?guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.386 m. The maximum transverse acceleration of a point at the middle of the segment is 8.40 * 103 m/s2 and the maximum transverse velocity is 3.80 m>s. (a) What is the amplitude of this standing wave? (b) What is the wave speed for the transverse traveling waves on this string?A piano's A-string should have fundamental frequency = 440 Hz. The string is 38.9 cm long and clamped at both ends. But the piano tuner finds that the string is flat, with frequency 436 Hz; so she increases the tension by 12 newtons to get 440 Hz. Find the linear mass density of the string and the tension when the string is correctly tuned. is 38.72 cm. 5.69x10^-3 kg/m 5.69x10^-3 kg/m Corrections for the data values: the incorrect frequency is 434.0 Hz, and the string length