A viola string with a fundamental frequency of D4 (293 Hz) is generally tuned using a tension of 49.0 N. However, just before a concert, the string breaks and only a G3 string (196 Hz) is available. The strings are the same length and are usually tuned with the same tension. What does the tension need to be on the replacement string to bring it up to the D4 frequency

Explanation:

For fundamental frequency in a vibrating string , the formula is

n = 1 / 2L  x  √ ( T /m₁ )

n is frequency , L is length , T is tension and m₁ is mass per unit length .

For first string ,

293 =  1 / 2L  x  √ ( 49 N  /m₁ )

For second string , let mass per unit length be m₂ .

196 =  1 / 2L  x  √ ( 49 N  /m₂ ) ( 1 )

To bring its frequency back to previous one let tension be T

293  =  1 / 2L  x  √ ( T  /m₂ ) ( 2 )

Dividing

293 / 196 = √ ( T  /49  )

1.4948 = √ ( T  /49  )

2.2344 = T  /49

T = 109.48 N .

To determine in which constellation the Sun is found at any time of the year.

Explanation:

Have located the stars in the various constellation. The Sun is found at any time in the year. Based on this the birth dates are determined for its meaning. But any year or every year the sun is found in the same place and same time. The various constellation connected to sun and earth are Sagittarius, Capricorn, Taurus, Gemini, Cancer, Aquarius, Pisces, Virgo, Libra and Scorpio, Aries. The constellation and date numbers are defined with appropriate meaning. For example, the Sun is found to be in Virgo from September 16 to October 31.