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Both 浪费 and 糟蹋 mean "to waste." (I'm not really concerned with the other uses of 糟蹋 right now.)
I've seen the collocations 糟蹋粮食 and 糟蹋人才, and 浪费 is very common in phrases like 浪费时间 and 浪费水.
Are there situations where both 浪费 and 糟蹋 are acceptable? Are they only applied to different types of things? Is there a tonal difference between the two words? (糟蹋 seems stronger, but 浪费粮食 and 浪费人才 also sound OK to me.)
糟蹋比浪费的语气更强烈。人们觉得很珍贵的物品被损坏或不被爱惜的使用了，通常是用糟蹋，而不会用浪费来形容。粮食可被浪费，可被糟蹋；人才可能被糟蹋，无法被浪费。
浪费：较为便宜的物品被损坏或不被爱惜的使用了，说话者觉得可惜但不心痛，会使用浪费这个词。
糟蹋：很贵重的物品被损坏或不被爱惜的使用了，说话者有心痛的情绪，才会使用糟蹋这个词。
糟蹋 has a stronger tone than 浪费. When people feel a valuable object is being damaged or is not being used with care, one would usually use 糟蹋, and not 浪费. 粮食 can be 浪费 or 糟蹋; 人才 could be 糟蹋, but is unable to be 浪费.
浪费: use when a relatively inexpensive object is being damaged or used without care, when the speaker feels it's a waste but not in a painful way.
糟蹋: use when a very valuable object is being damaged or used without care, or when the speaker feels pained.
I came across this dictionary 《小學生的國語辭典》(精)(小贏家) approved by the Taiwanese Ministry of Education for primary school students:
糟蹋:任意浪費,不加以愛惜。 例:不要糟蹋糧食。請注意:「糟蹋」和「浪费」都有任急耗費不加以愛惜的意思,但是有分別:「糟蹋」除了指浪費外,還指損壞、任意破壞:「浪費」指的是人力、財力、時間沒有好好運用,和「節約」、「節省」相反。「糟蹋」的語意比「浪賨」重。
Translated:
Both terms contain the meaning of indiscriminate wastage and not treasuring of the subject. But there is a distinction in that 糟蹋, besides possessing the meaning of 浪費, also includes some form of ruining or destroying at will.
糟蹋 is a much stronger term to use than 浪費.
Examples:
这个数学题很难，浪费了我不少时间。
I wasted quite some time attempting this difficult maths question.
这蛋糕你不吃就算，别把它给糟蹋了。
Please don't ruin the cake if you don't want to eat it.
if you hate the subject, use 糟蹋。 the subject is used to be considered as cheaper than the object. Or you have sympathy with the object, you can use 糟蹋.
浪费 means waste,while 糟蹋 kind of means destroy. 浪费 has a more board use than 糟蹋. You just have to remember the situation when 糟蹋 will be used.
我舍不得那么糟蹋粮食
糟蹋我的妻和女
自己家乡受糟蹋
